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Complexity of an SIR epidemic dynamics model with impulsive vaccination control. (English) Zbl 1065.92050
Summary: This paper considered an infected class – removed class (IR) epidemic model with impulsive vaccination, which may inherently oscillate. We studied the impulsive control and got conditions by which the epidemics elimination solution is globally asymptotically stable and conditions for the boundedness of the system. On the other hand, if the epidemic turns out to be endemic, we studied numerically the influence of impulsive vaccination on the periodic oscillations of the system without impulsions and found phenomena of chaos in this case.

##### MSC:
 92D30 Epidemiology 34A37 Ordinary differential equations with impulses 93C15 Control/observation systems governed by ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 37N25 Dynamical systems in biology
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